Find the value of $\frac{\sin 25°}{\cos 65°} + \frac{\tan 23°}{cot 67°}$

We know that 𝑠𝑖𝑛 θ = 𝑐𝑜𝑠 (90 − θ), where θ is any angle. Also, 𝑡𝑎𝑛 θ = 𝑐𝑜𝑡 (90 − θ).

So, from the question,

$\frac{\sin 25°}{\cos 65°} + \frac{\tan 23°}{cot 67°}$ = $\frac{\cos (90°- 25°)}{\cos 65°} + \frac{cot(90°- 23°)}{cot 67°}$

                                     = $\frac{\cos 65°}{\cos 65°} + \frac{cot 67°}{cot 67°}$

                                     = 1 +  1 = 2